# chp32_5 - π f with T = 1/f Planets further from the sum...

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PHY2061 R. D. Field Department of Physics chp32_5.doc University of Florida Circular Motion: Magnetic vs Gravitational Planetary Motion: For circular planetary motion the force on the orbiting planet is equal the mass times the centripetal acceleration , a = v 2 /r , as follows: F G = GmM/r 2 = mv 2 /r Solving for the radius and speed gives, r = GM/v 2 and v = (GM/r) 1/2 . The period of the rotation ( time it takes to go around once ) is given by T=2 π r/v=2 π GM/v 3 or T GM r = 2 32 π / . The angular velocity , ω = d θ /dt , and linear velocity v = ds/dt are related by v = r ω , since s = r θ . Thus, 2 / 3 / r GM = ω . The angular velocity an period are related by T = 2 π / ω and the linear frequency f and ω are related by ω ω = 2
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Unformatted text preview: π f with T = 1/f . Planets further from the sum travel slower and thus have a longer period T . Magnetism: For magnetic circular motion the force on the charged particle is equal its mass times the centripetal acceleration , a = v 2 /r , as follows: F B = qvB = mv 2 /r . Solving for the radius and speed gives, r = mv/(qB) = p/(qB) , and v = qBr/m . The period of the rotation is given by T = 2 π r/v = 2 π m/(qB) and is independent of the radius ! The frequency ( called the cyclotron frequency ) is given by f = 1/T= qB/(2 π m) is the same for all particles with the same charge and mass ( ω = qB/m ) . M m v r v r B-in q...
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